Optimal invariant detection for DS-SS signals

This paper focuses on optimal detection of quadrature phase-shift keying (QPSK) and binary phase-shift keying (BPSK) direct sequence spread spectrum (DS-SS) signals in additive white Gaussian noise (AWGN) with unknown spreading sequence and other parameters. Using complex Gaussian mixture signal model and invariance principle, we derive constant-false-alarm-rate (CFAR) invariant detectors such as uniformly most powerful invariant (UMPI) tests and other sub-optimal invariant tests. As low computational complexity approximation of UMPI test under low signal-noise-ratio (SNR), locally most powerful invariant (LMPI) tests are also derived. Simulation results illustrate the performance of the proposed detectors and compare them for the cases of QPSK and BPSK signals.